REAL WORLD DATA ON GRAPHING CALCULATORS:
CONCEPTS: Data can be stored in a TI-8X graphing calculator as variables (numbers assigned to letters), matrices, lists (STAT) , and equations (Y=).
Data can be graphed on a TI-8x graphing calculator from lists (STATPLOT), equations (Y=) or Draw objects (Draw).
For science, we most often use real world data, and then analyze it using graphs and/or equations.
Data is stored in lists, much like a spreadsheet. Each column is given a name (L1 through L6).. (more names are definable on TI-83 pluses and beyond).
[STAT] [EDIT] can be reached by pressing the [STAT] key, then either [1] or [ENTER].
Practice by inputting into
L1L2
12
25
56
88
119
2215
3526
using the arrows and enter key. To clear a list, use the up arrow to go to the top line, and hit the [CLEAR] key. ([DEL] will erase the list, and then it will have to be reinserted!). This can also be used to make one list equal another. To erase a single list entry, go over it and hit the [DEL] key. It is important to make sure that there are the same number of entries in L1 and L2. Using L1 and L2 is a good idea, since many other commands assume that you are using those lists by default.
To view your data plotted on a graph, hit the [2nd] [STAT PLOT] key, which is above the [Y=] key. Up to three simaltaneous sets of data can be plotted as once. Select [1], and enter upon the On, use the arrows to move to the scatter plot or line plot function, and enter. For the Xlist variable, enter [2nd] [L1] (above the [1] key), and for the Ylist variable, enter [2nd] [L2] (above the [2] key). Choose a thin dot for a mark, and hit enter.
To view the graph, hit the [GRAPH] key. The data is plotted, yet the window may not be correct. To set the graph axes, hit the [WINDOW] key.... too much work! Hit the [ZOOM] key. Using the arrows, move down to 9: ZoomStat. This will automatically calculate the correct window to best fit all your data. Shortcut is to hit [ZOOM][9]. Other options under the Zoom menu allow you to resize the graph window. To set other options for the window hit the [FORMAT] key. Usually you would want to set Rectangular coordinates, Coordinates On, Grid Off (takes too long to draw), Axes On, Label On, and Expression On.
Hit [Zoom][9] to get the graph again. Using the [TRACE] key allows you to trace along the data.
TO ANALYZE THE DATA: Analyzing real world data is done using the [STAT] [CALC] Menu. Hit the [STAT] key, then use the arrows to move to the [CALC] menu. Option 2 will give 2 variable statistics for both lists, use the arrows to see all the information.
Finding the “trend” of the data is the whole purpose of science, of course. This is known as a regression Equation, or in Algebra I, a best fit line. Option 4: LinReg [ENTER] will give a linear equation as y=mx+b for L1 and L2. Other lists can be used by typing their names in after the command.
The r is the correlation coefficient between 1 and –1. Anything below .90 is probably not a good fit.
To see this “best fit” line on the same graph as the data requires graphing an equation using the [Y=] key.
Three ways are available to enter this equation:
1. Manually typing it in under Y1= .647 X + 2.37
2. Hitting the [Y=] key, then having the calculator enter the equation, which is stored in the RegEq variable by entering [VARS], 5:Statistics, > EQ, 1:RegEq [ENTER].
3. Telling the calculator to enter the equation into Y1 variable when calculating it. [STAT], > CALC, 4: LinEq then [VARS], > Y-VARS, 1: Function, 1:Y1
The names of any variable or key command, RegEq, etc... can be accessed from a TI-83 by using the [2nd] [CATALOG] function, then the ALPHA key of the first letter.
Type the [Y=] key to see the equation in the Y1= variable. Up to 10 equations can be plotted simultaneously along with the 4 statplots. Use the arrows to make sure that the = sign is highlighted, this will indicate that this equation is plotted on the graph. Hitting Enter toggles its state. Hitting Enter on the symbol to the left of the Y1 changes the type of line drawn: thinline, thickline, greaterthan, lessthan, moving point, dashed line.
Hit [ZOOM][9] to see both the data and the best fit line on the same graph.
We have now entered real world data and analyzed it!!
The CBL programs will do all this for you, but is important for you to know the concepts behind the programs